Entropy (information theory)In information theory, the entropy of a random variable is the average level of "information", "surprise", or "uncertainty" inherent to the variable's possible outcomes. Given a discrete random variable , which takes values in the alphabet and is distributed according to : where denotes the sum over the variable's possible values. The choice of base for , the logarithm, varies for different applications. Base 2 gives the unit of bits (or "shannons"), while base e gives "natural units" nat, and base 10 gives units of "dits", "bans", or "hartleys".
Green buildingGreen building (also known as green construction or sustainable building) refers to both a structure and the application of processes that are environmentally responsible and resource-efficient throughout a building's life-cycle: from planning to design, construction, operation, maintenance, renovation, and demolition. This requires close cooperation of the contractor, the architects, the engineers, and the client at all project stages. The Green Building practice expands and complements the classical building design concerns of economy, utility, durability, and comfort.
Cross-entropyIn information theory, the cross-entropy between two probability distributions and over the same underlying set of events measures the average number of bits needed to identify an event drawn from the set if a coding scheme used for the set is optimized for an estimated probability distribution , rather than the true distribution . The cross-entropy of the distribution relative to a distribution over a given set is defined as follows: where is the expected value operator with respect to the distribution .
House Energy RatingThe House Energy Rating (HER) or House Energy Rating Scheme (HERS) are worldwide standard measures of comparison by which one can evaluate the energy efficiency of a new or an existing building. The comparison is generally done for energy requirements for heating and cooling of indoor space. The energy is the main criterion considered by any international building energy rating scheme but there are some other important factors such as production of greenhouse gases emission, indoor environment quality, cost efficiency and thermal comfort, which are considered by some schemes.
Mutual informationIn probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual dependence between the two variables. More specifically, it quantifies the "amount of information" (in units such as shannons (bits), nats or hartleys) obtained about one random variable by observing the other random variable. The concept of mutual information is intimately linked to that of entropy of a random variable, a fundamental notion in information theory that quantifies the expected "amount of information" held in a random variable.
Low-energy houseA low-energy house is characterized by an energy-efficient design and technical features which enable it to provide high living standards and comfort with low energy consumption and carbon emissions. Traditional heating and active cooling systems are absent, or their use is secondary. Low-energy buildings may be viewed as examples of sustainable architecture. Low-energy houses often have active and passive solar building design and components, which reduce the house's energy consumption and minimally impact the resident's lifestyle.
Joint entropyIn information theory, joint entropy is a measure of the uncertainty associated with a set of variables. The joint Shannon entropy (in bits) of two discrete random variables and with images and is defined as where and are particular values of and , respectively, is the joint probability of these values occurring together, and is defined to be 0 if . For more than two random variables this expands to where are particular values of , respectively, is the probability of these values occurring together, and is defined to be 0 if .
Energy conservationEnergy conservation is the effort to reduce wasteful energy consumption by using fewer energy services. This can be done by using energy more effectively (using less energy for continuous service) or changing one's behavior to use less service (for example, by driving less). Energy conservation can be achieved through efficient energy use, which has some advantages, including a reduction in greenhouse gas emissions and a smaller carbon footprint, as well as cost, water, and energy savings.
Zero-energy buildingA Zero-Energy Building (ZEB), also known as a Net Zero-Energy (NZE) building, is a building with net zero energy consumption, meaning the total amount of energy used by the building on an annual basis is equal to the amount of renewable energy created on the site or in other definitions by renewable energy sources offsite, using technology such as heat pumps, high efficiency windows and insulation, and solar panels. The goal is that these buildings contribute less overall greenhouse gas to the atmosphere during operations than similar non-ZNE buildings.
Information theoryInformation theory is the mathematical study of the quantification, storage, and communication of information. The field was originally established by the works of Harry Nyquist and Ralph Hartley, in the 1920s, and Claude Shannon in the 1940s. The field, in applied mathematics, is at the intersection of probability theory, statistics, computer science, statistical mechanics, information engineering, and electrical engineering. A key measure in information theory is entropy.
Deep energy retrofitA Deep energy retrofit (abbreviated as DER) can be broadly categorized as an energy conservation measure in an existing building also leading to an overall improvement in the building performance. While there is no exact definition for a deep energy retrofit, it can be defined as a whole-building analysis and construction process, that aims at achieving on-site energy use minimization in a building by 50% or more compared to the baseline energy use (calculated using utility bills analysis) making use of existing technologies, materials and construction practices.
Measurement in quantum mechanicsIn quantum physics, a measurement is the testing or manipulation of a physical system to yield a numerical result. A fundamental feature of quantum theory is that the predictions it makes are probabilistic. The procedure for finding a probability involves combining a quantum state, which mathematically describes a quantum system, with a mathematical representation of the measurement to be performed on that system. The formula for this calculation is known as the Born rule.
Building performance simulationBuilding performance simulation (BPS) is the replication of aspects of building performance using a computer-based, mathematical model created on the basis of fundamental physical principles and sound engineering practice. The objective of building performance simulation is the quantification of aspects of building performance which are relevant to the design, construction, operation and control of buildings. Building performance simulation has various sub-domains; most prominent are thermal simulation, lighting simulation, acoustical simulation and air flow simulation.
Quantities of informationThe mathematical theory of information is based on probability theory and statistics, and measures information with several quantities of information. The choice of logarithmic base in the following formulae determines the unit of information entropy that is used. The most common unit of information is the bit, or more correctly the shannon, based on the binary logarithm.
Differential entropyDifferential entropy (also referred to as continuous entropy) is a concept in information theory that began as an attempt by Claude Shannon to extend the idea of (Shannon) entropy, a measure of average (surprisal) of a random variable, to continuous probability distributions. Unfortunately, Shannon did not derive this formula, and rather just assumed it was the correct continuous analogue of discrete entropy, but it is not. The actual continuous version of discrete entropy is the limiting density of discrete points (LDDP).
MeasurementMeasurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events. In other words, measurement is a process of determining how large or small a physical quantity is as compared to a basic reference quantity of the same kind. The scope and application of measurement are dependent on the context and discipline. In natural sciences and engineering, measurements do not apply to nominal properties of objects or events, which is consistent with the guidelines of the International vocabulary of metrology published by the International Bureau of Weights and Measures.
Energy auditAn energy audit is an inspection survey and an analysis of energy flows for energy conservation in a building. It may include a process or system to reduce the amount of energy input into the system without negatively affecting the output. In commercial and industrial real estate, an energy audit is the first step in identifying opportunities to reduce energy expense and carbon footprint. When the object of study is an occupied building then reducing energy consumption while maintaining or improving human comfort, health and safety are of primary concern.
Conditional entropyIn information theory, the conditional entropy quantifies the amount of information needed to describe the outcome of a random variable given that the value of another random variable is known. Here, information is measured in shannons, nats, or hartleys. The entropy of conditioned on is written as . The conditional entropy of given is defined as where and denote the support sets of and . Note: Here, the convention is that the expression should be treated as being equal to zero. This is because .
Entropy estimationIn various science/engineering applications, such as independent component analysis, , genetic analysis, speech recognition, manifold learning, and time delay estimation it is useful to estimate the differential entropy of a system or process, given some observations. The simplest and most common approach uses histogram-based estimation, but other approaches have been developed and used, each with its own benefits and drawbacks.
Information gain (decision tree)In information theory and machine learning, information gain is a synonym for Kullback–Leibler divergence; the amount of information gained about a random variable or signal from observing another random variable. However, in the context of decision trees, the term is sometimes used synonymously with mutual information, which is the conditional expected value of the Kullback–Leibler divergence of the univariate probability distribution of one variable from the conditional distribution of this variable given the other one.
